Question

How do I solve equations bt extracting square roots?Ex.7B2%7D%20%20%3D%208" id="TexFormula1" title="3(x + {4)}^{2} = 8" alt="3(x + {4)}^{2} = 8" align="absmiddle" class="latex-formula">
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Answer 1

Answer:

$x=\frac{2\sqrt{6}}{3}-4,\:x=-\frac{2\sqrt{6}}{3}-4$

Step-by-step explanation:

$3(x+4)^2 =8\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\frac{3\left(x+4\right)^2}{3}=\frac{8}{3}\\\\Simplify\\\left(x+4\right)^2=\frac{8}{3}\\\\\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}\\g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\mathrm{Solve\:}\:x+4=\sqrt{\frac{8}{3}}:\\\quad x=\frac{2\sqrt{6}}{3}-4\\\\\\\mathrm{Solve\:}\:x+4=-\sqrt{\frac{8}{3}}:\\\quad x=-\frac{2\sqrt{6}}{3}-4$

$x=\frac{2\sqrt{6}}{3}-4,\:x=-\frac{2\sqrt{6}}{3}-4$